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# C. Prove the following (you can use any formal induction/other theoretical method, A means power here): i. ii. iii. What is the time complexity

## C. Prove the following (you can use any formal induction/other theoretical method, "A" means power here): i. ii. iii. What is the time complexity recurrence relation for Fibonacci numbers? Explain it with the subproblems and size of sub-problems. Show the time complexity derivation using the telescoping method. (4 marks) Show that 2n^3+5n^2+6n+ 18 is in Theta (n^3). (2 marks) 5+2cos(n) Theta (1) (2 marks) iv. Show that (3/2)n^2+2n-3 = 2 (n^2) (2 marks) V. Show that n^3+5n is not O(n^2) (2 marks). vi. vii. T(n) = 2T (n/2)+n = O(n) (2 marks) T(n)T(n/4)+T(5n/8) n = O(n) (2 marks)

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i The time complexity recurrence relation for Fibonacci numbers is Tn Tn1 Tn2 O1 This relation represents the recursive formula for Fibonacci numbers Fn Fn1 Fn2 The O1 term represents the constant tim...### Get Instant Access to Expert-Tailored Solutions

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